## Saturday, October 26, 2013

### Improvements Graphing Piecewise Functions

My PreCalc kids did better graphing piecewise functions this year than in the past, so there's a chance I actually improved at teaching this topic.  Just a couple notes (more for myself, so I don't forget this next year):

1. Draw a vertical, dotted "wall" at the possible point of discontinuity.
2. Determine which piece(s) of your function will have a closed circle at your wall and which one(s) will have an open circle.
3. Determine which function you'll use for all your x's to the left of the wall and which function you'll use for the right.
4. Graph the top function (use transformations); erase everything to the left or the right of your wall, depending on your decision from Step 3.
5. Repeat Step 4 for the bottom function.  Erase the oppose piece this time.

The key, for me, is "the wall."  I've used this concept before in analyzing limits in calculus graphically, but I don't know why it didn't dawn on me to use the same concept here until recently.  It worked like a charm--hardly any students drew the nonsensical, non-function relations that I've seen in the past.  Also, hopefully this gives us a leg up when we get to limits next semester.  Fingers crossed!